What are the solutions to the equation 1/4 x^2+3x-3=0 ?

The solutions to the equation 1/4 x^2+3x-3=0 are x=2(2sqrt(3)-3),x=-2(3+2sqrt(3))

Find the zeros of 1/4 x^2+3x-3=0

The zeros of 1/4 x^2+3x-3=0 are x=2(2sqrt(3)-3),x=-2(3+2sqrt(3))

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\frac{1}{4} x^{2} + 3 x - 3 = 0

x = 2 (23 - 3), x = - 2 (3 + 23)

Decimal Notation

x = 0.92820 \dots, x = - 12.92820 \dots

Solution steps

\frac{1}{4} x^{2} + 3 x - 3 = 0

Multiply both sides by

4

x^{2} + 12 x - 12 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 1 \cdot ( - 12 )}{2 \cdot 1}

1 2^{2} - 4 \cdot 1 \cdot (- 12) = 83

x_{1, 2} = \frac{- 12 \pm 8 3}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 12 + 8 3}{2 \cdot 1}, x_{2} = \frac{- 12 - 8 3}{2 \cdot 1}

x = \frac{- 12 + 8 3}{2 \cdot 1} : 2 (23 - 3)

x = \frac{- 12 - 8 3}{2 \cdot 1} : - 2 (3 + 23)

The solutions to the quadratic equation are:

x = 2 (23 - 3), x = - 2 (3 + 23)

22 x = 12 x^{2} + 6

y^{2} + 13 = 8 y

9 x^{2} = - 24 x - 10

x, x^{2} + 2 x - 35 = 0

1 = x^{2} + x

What are the solutions to the equation 1/4 x^2+3x-3=0 ?
The solutions to the equation 1/4 x^2+3x-3=0 are x=2(2sqrt(3)-3),x=-2(3+2sqrt(3))
Find the zeros of 1/4 x^2+3x-3=0
The zeros of 1/4 x^2+3x-3=0 are x=2(2sqrt(3)-3),x=-2(3+2sqrt(3))